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  • Research Article
  • Open Access

The High-Resolution Rate-Distortion Function under the Structural Similarity Index

  • 1Email author,
  • 2 and
  • 3
EURASIP Journal on Advances in Signal Processing20102011:857959

  • Received: 15 July 2010
  • Accepted: 1 November 2010
  • Published:


We show that the structural similarity (SSIM) index, which is used in image processing to assess the similarity between an image representation and an original reference image, can be formulated as a locally quadratic distortion measure. We, furthermore, show that recent results of Linder and Zamir on the rate-distortion function (RDF) under locally quadratic distortion measures are applicable to this SSIM distortion measure. We finally derive the high-resolution SSIM-RDF and provide a simple method to numerically compute an approximation of the SSIM-RDF of real images.


  • Image Processing
  • Information Technology
  • Recent Result
  • Quantum Information
  • Similarity Index

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Authors’ Affiliations

Department of Electronic Systems, Aalborg University, 9220 Alborg, Denmark
Department of Electronic Engineering, Federico Santa María Technical University, 2390123 Valparaíso, Chile
PacketVideo Corporation, San Diego, CA 92121, USA


© Jan Østergaard et al. 2011

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.